Title:

Similarity on intuitionistic fuzzy sets and the Jaccard coefficient

Subtitle:

Raport Badawczy = Research Report ; RB/54/2003

Creator:

Szmidt, Eulalia : Autor ; Kacprzyk, Janusz (1947– ) : Autor

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Date issued/created:

2003

Description:

[8] pages ; 21 cm ; Bibliography p. [7,8]

Type of object:

Book/Chapter

Subject and Keywords:

Fuzzy sets ; Jaccard coefficient

Abstract:

In this article we propose a new measure of similarity for intuitionistic fuzzy sets. The most commonly used similarity measures are just the coun­terparts of distances in the sense that dissimilarity is proportional to a dis­tance between objects (elements, ...). The measure we propose ’’weights” both similarity and dissimilarity (un­der the assumption that dissimilarity behaves like a distance function be­tween the objects). In other words, we take into account two kinds of a distance function: a distance function between an element/object X we com­pare and an element/object F we com­pare with, and a distance function be­tween an element/object X we com­pare and a complement Fc of an el­ement/object we compare with. We also examine a special case of the pro­posed similarity measure (entropy in the sense of De Luca and Termini ax­ioms) and show that this special case is a counterpart of the Jaccard coeffi­cient.In this article we propose a new measure of similarity for intuitionistic fuzzy sets. The most commonly used similarity measures are just the coun­terparts of distances in the sense that dissimilarity is proportional to a dis­tance between objects (elements, ...). The measure we propose ’’weights” both similarity and dissimilarity (un­der the assumption that dissimilarity behaves like a distance function be­tween the objects). In other words, we take into account two kinds of a distance function: a distance function between an element/object X we com­pare and an element/object F we com­pare with, and a distance function be­tween an element/object X we com­pare and a complement Fc of an el­ement/object we compare with. We also examine a special case of the pro­posed similarity measure (entropy in the sense of De Luca and Termini ax­ioms) and show that this special case is a counterpart of the Jaccard coeffi­cient.In this article we propose a new measure of similarity for intuitionistic fuzzy sets. The most commonly used similarity measures are just the coun­terparts of distances in the sense that dissimilarity is proportional to a dis­tance between objects (elements, ...). The measure we propose ’’weights” both similarity and dissimilarity (un­der the assumption that dissimilarity behaves like a distance function be­tween the objects). In other words, we take into account two kinds of a distance function: a distance function between an element/object X we com­pare and an element/object F we com­pare with, and a distance function be­tween an element/object X we com­pare and a complement Fc of an el­ement/object we compare with. We also examine a special case of the pro­posed similarity measure (entropy in the sense of De Luca and Termini ax­ioms) and show that this special case is a counterpart of the Jaccard coeffi­cient.

Relation:

Raport Badawczy = Research Report

Resource type:

Text

Detailed Resource Type:

Report

Source:

RB-2003-54

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

Original in:

Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

Access:

Open